High frequency vibration control using piezoelectric patch transducers

Abstract

Engineering systems such as aircrafts, ships and automotive are built-up structures fabricated from many components that can be classified as deterministic substructure (DS) and non-deterministic substructure (Non-DS). Non-DSs are subjected to short wavelength deformation, producing response that cannot be described mathematically using deterministic method. This makes vibration control effort difficult due to the combined modal response which produce no visible distinct peaks, with addition of the response being very sensitive to structural uncertainties. Piezoelectric (PZT) transducer connected to a shunt circuit is an attractive choice to attempt vibration attenuation of a Non-DS due to its ability to be fully passive thus ensuring stability, in addition of having high-strength and small-volume properties. Using Hybrid modelling equation (a method commonly used to model and analyse high-frequency vibration response), it is determined that to achieve maximum power dissipation from a Non-DS using PZT shunt damper, the shunt circuit needs to be designed such that the impedance is complex conjugate of its inherent capacitance parallel with impedance faced by the host structure at the connection area. In the first part of this research, the impedance faced by the Non-DS at the connection area is estimated using effective line mobility of an infinite thin plate under moment excitation by a square PZT patch using double integration of the infinite mobility which resulted to a hypergeometric function. The analytical model is compared with the average response of a randomized finite thin plate via Monte Carlo simulation which managed to significantly cut computational time to ~40 times shorter compared to using the finite method. Using findings from this part, the implementation of the designed shunt circuit using physical electronic components is carried out. One possible circuit configuration that closely resembles the theoretical impedance derived is realized by application of two negative impedance converters (NICs) utilizing op-amps, in order to replicate the circuit components with negative impedance values. Through parametric studies, it is shown that that the more PZT shunt dampers are attached to its non-deterministic host structure, the more energy can be dissipated from the system. By using different patch size for the shunt damper, it is shown that patch with larger size resulted to better energy reduction of the Non-DS; bearing in mind that cut-off frequency will occur earlier for bigger patch due to the bending wavelength limitation. Parametric study using different patch configuration shows that no conclusive difference can be seen for energy reduction of the plate when the patch is connected in series, parallel or independent. However, considering the complexity of the circuit needed to be designed when more patches are used for series and parallel arrangements, this work will focus on independent PZT shunt damper design where each patch is connected to its own shunt circuit. Experiments are conducted via real lab measurements or virtually using finite element software to validate the findings. From this research, the analytical solution for the optimal shunt circuit of a PZT shunt damper to attenuate the highest energy from a structure vibrating at high frequency range has been derived and shown. Findings from this research can serve as a guide for future researches in high-frequency structural vibration control.